Unit 16
Positional Constraint Deduction
About this unit
Assign items, people, or objects to specific positions or slots by satisfying a set of explicit placement rules. Unlike general ordering, these questions give hard constraints: "must be directly adjacent", "must be in position 1", "must be exactly 2 apart" — and you must find the unique valid configuration.
What types of questions will you face?
- 1Assign 4-6 coloured boxes/bags in a row where specific pairs must be adjacent or a set distance apart
- 2Stack 5 ingredients in a sandwich/lunchbox where each layer is constrained relative to others
- 3Assign people to car seats (driver, passenger, back left, back right) under strict constraints
- 4Identify which locker or position holds the prize using adjacency and distance clues
- 5Seat 6+ people at a rectangular table with row, column, and opposite-seat rules
- 6Assign departments to building floors under a full set of ordering and adjacency constraints
Skills you will build
- Applying hard adjacency constraints ("only next to", "directly above/below")
- Handling absolute constraints ("must be in position 1 or 2") alongside relative ones
- Building up valid assignments incrementally — start with the most constrained element
- Eliminating invalid arrangements quickly using a single violated constraint
- Tracking "exactly N positions away" constraints on a numbered row
- Applying both linear and 2D grid positional rules simultaneously
By the end of this unit, you will be able to
- Solve any hard-constraint placement puzzle by starting from the most restricted element
- Find the unique valid configuration when every position is tightly constrained
- Assign seats, layers, or positions efficiently without checking every possibility
- Distinguish solvable from unsolvable configurations when given partial constraints
Difficulty profile
The hardest unit in the course (avg 3.92). Simple 4-element row problems are Medium; 6-element rows with multiple adjacency, distance, and direction constraints plus table-seating problems are Very Difficult. This unit rewards systematic, patient work.
Exam tip: Positional Constraint Deduction
Always start with the element that has the most explicit constraints (e.g. "must be in position 1", "only adjacent to X"). Place it first, then use each constraint to narrow what the remaining positions can contain. Never guess — build the solution one forced step at a time.
Sample Questions
Stacking puzzles start with anchors: fix the bottom layer, lock the “directly on top of” pair as one block, then add layers while checking “must not touch”.
Vertical stack items appear in the medium band of Selective TS — students who place the locked pair first avoid trying every permutation.
The examiner checks whether you can build the only valid bottom-to-top order using a fixed base, one consecutive pair, and non-adjacency bans.
Five layers from bottom to top. One item is fixed at the base. One pair must be consecutive. Some pairs cannot be adjacent. You name the top layer.
Best approach: Layer 1 = given bottom. Treat [turkey][cream cheese] as a block. Slot remaining items between rules; any touch between banned neighbours eliminates that try.
Question
Sam stacks five items in a lunchbox (each is one layer, from bottom to top): wrap, turkey, spinach, tomato, and cream cheese.
Rules:
- Wrap is the bottom layer.
- Tomato must not touch cream cheese.
- Spinach must not touch tomato.
- Cream cheese sits directly on top of the turkey.
Which item is on top?
- Aspinach
- Btomato
- Cturkey
- Dcream cheese
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Car-seat grids need a sketch: “next to” = same row; “directly behind” = same column in the back row — mix those up and every deduction fails.
2×2 seating layouts recur on Selective mocks in the medium band — draw the grid before placing anyone with an either-or clue.
You must translate spatial words into seat positions, place the most constrained person first, and resolve either-or options without breaking “not beside” rules.
Four people, driver + passenger + two back seats. Clues include behind-driver, not in back, not beside someone, and either-or seat choices.
Best approach: Draw front-left / front-right / back-left / back-right. Put Quinn behind the driver first. Test Pia’s either-or; use “Ravi not beside Sasha” to rule out Pia in the back.
Question
Four friends sit in a car with two seats in front and two in the back.
- Pia is either driving or sitting beside Quinn.
- Quinn sits directly behind the driver.
- Ravi is not in the back and is not sitting beside Sasha.
Who is driving?
- AQuinn
- BRavi
- CPia
- DSasha
Decided on your answer? Check how you went below.
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